Practice using Pascal's Triangle and the Binomial Theorem to expand expressions, find coefficients, and connect patterns to combinations.
Read each problem carefully. Show your work in the space provided. Use Pascal's Triangle or the Binomial Theorem when helpful.
Expanding binomials and finding coefficients
Math - Grade 9-12
- 1
Write rows 0 through 5 of Pascal's Triangle. Remember that row 0 is the single number 1.
- 2
Use Pascal's Triangle to expand (x + y)^4.
- 3
Use Pascal's Triangle to expand (a + b)^5.
- 4
Expand (2x + 3)^3 completely.
- 5
Find the coefficient of x^3 in the expansion of (x + 2)^5.
- 6
Use the Binomial Theorem to find the fourth term of (3x - 2)^6 when written in descending powers of x.
- 7
Find the missing entries in this row of Pascal's Triangle: 1, 7, __, __, __, __, 7, 1.
- 8
Explain why the coefficients in the expansion of (x + y)^n add up to 2^n.
- 9
Find the sum of the coefficients in the expansion of (2x - 5)^8.
- 10
Find the coefficient of x^4 in the expansion of (x - 3)^7.
- 11
A student claims that the middle number in row 8 of Pascal's Triangle is 56. Check the claim and explain whether it is correct.
- 12
Use the Binomial Theorem to write the general term of (a + b)^n, then use it to identify the term containing a^2b^5 in (a + b)^7.